NBA Court Realty

Dan Cervone
May 6, 2016

The Basketball Court is a Real Estate Market

Space is a valuable commodity in basketball.

During a possession:

  • Players own (occupy) different court space.
  • Players compete for space.
  • Through movement, players exchange space.

The Basketball Court is a Real Estate Market

How do we quantify:

  • Which space is most important? And to whom?
  • Who has the upper hand in the battle over floor space?
  • How do different teams/players value space differently?
  • Impact of personnel, matchups, etc. on court spacing.

Who's got the most valuable property?


Player's real estate investment portfolio value:

  • Who the player is
  • Where he is
  • How open he is, what space he controls

vor

What space does a player control?

“Weighted Voronoi'' model:

  • Players own their exact location
  • Invested'' in areas they're closest to

vor

Weighted Voronoi details

Specifically: divide the court into \( M \) equally sized cells

  • \[ w^i_j(t) = \text{dist}(\text{player } i, \text{cell } j) \] at time \( t \)

\[ x^i_j(t) = \begin{cases} \frac{1}{1 + w^i_j(t)} & i = \text{argmin}_h w^h_j(t) \\ 0 & \text{otherwise} \end{cases} \]

  • \( \beta \in \mathbb{R}^M \), where \( \beta_j \) is price/value of region \( j \)
  • \( X^i(t) \) row vector, entry \( j \) is \( x^i_j(t) \).
  • \( X^i(t) \beta \) is the total property value of player \( i \) at time \( t \)

Inferring court property values


Idea: Passes move the ball to more valuable real estate

  • Player C passes to player A
  • Player A's portfolio value \( > \) player C's
  • We can infer value of every piece of court space using passing data


vor2

Inferring court property values


Passes move the ball to more valuable real estate

  • Player C passes to player A
  • Player A's portfolio value \( > \) player C's
  • We can infer value of every piece of court space using passing data


wvor2

Inferring court property values

\( \beta \) is estimated using a penalized Plackett-Luce model.

  • \( P(i \rightarrow j | i \rightarrow j \text{ or } j \rightarrow i) \propto \exp(X^j(t)\beta) \)
  • \[ \begin{align} L_{\lambda}(\beta) =& \Bigg[ \sum_{i, j} \sum_{t : \text{pass } i \rightarrow j} X^j(t)\beta - \log\Big( \exp \big(X^i(t)\beta \big) + \exp \big( X^j(t)\beta \big) \Big) \Bigg] \\ & \hspace{2cm} - \frac{1}{2}\lambda ||\beta||_2^2 \\ & \text{ subject to } \beta_m \geq 0, \: m=1, \ldots, M \nonumber \end{align} \]

Inferring court property values

Player- (team-) specific property values (\( \beta + \alpha^i \))

\[ \begin{align} L_{\lambda_1, \lambda_2}(\beta, \alpha^1, \ldots, \alpha^K) = & \\ & \hspace{-6cm} \Bigg[ \sum_{i, j} \sum_{t : \text{pass } i \rightarrow j} X^j(t)(\beta + \alpha^j) - \log\Big( \exp \big(X^i(t)(\beta + \alpha^i) \big) + \exp \big( X^j(t)(\beta + \alpha^j) \big) \Big) \Bigg] \nonumber \\ & \hspace{2cm} - \frac{1}{2}\lambda_1 ||\beta||_2^2 - \frac{1}{2}\lambda_2 \sum_i ||\alpha^i||_2^2 \\ & \text{ subject to } \beta_k \geq 0, \: k=1, \ldots, M. \nonumber \end{align} \]

Real estate maps

Real estate maps

Possession views

NBA Optical Tracking Data

Spacing metrics

Warriors 2014-15

Player on.ball.self off.ball.self on.ball.teammates
Marreese Speights 2.46 2.29 8.51
David Lee 2.07 1.97 8.42
Andrew Bogut 1.91 1.95 8.56
Draymond Green 1.89 1.89 8.55
Harrison Barnes 1.87 2.46 8.34
Klay Thompson 1.81 2.36 8.50
Leandro Barbosa 1.52 2.24 8.38
Shaun Livingston 1.47 1.91 8.51
Andre Iguodala 1.41 2.30 8.50
Stephen Curry 1.03 1.78 8.54
  • on.ball.self: Players' avg. portfolio value when ballcarrier.
  • off.ball.self: Players' avg. portfolio value when NOT ballcarrier.
  • on.ball.teammates: Teammates' avg. portfolio value when player is ballcarrier.

Spacing metrics

Cavaliers 2014-15

Player on.ball.self off.ball.self on.ball.teammates
Kevin Love 2.46 2.34 8.65
Timofey Mozgov 2.33 2.22 8.71
Shawn Marion 2.06 2.39 8.72
Tristan Thompson 2.03 2.05 8.76
J.R. Smith 1.89 2.42 8.66
Dion Waiters 1.85 2.50 8.65
LeBron James 1.80 1.99 8.73
Iman Shumpert 1.69 2.46 8.65
Kyrie Irving 1.38 2.01 8.84
Matthew Dellavedova 1.25 2.06 8.59
  • on.ball.self: Players' avg. portfolio value when ballcarrier.
  • off.ball.self: Players' avg. portfolio value when NOT ballcarrier.
  • on.ball.teammates: Teammates' avg. portfolio value when player is ballcarrier.

Todo 1: more interesting metrics

More situational metrics:

  • Changing one player in a lineup
  • Metrics by court region or participation level in a play

Connections with game events:

  • Characterize ball movement and shooting using RE values.
  • Game- or possession-level RE stats map to outcomes?

Todo 2: less hacky modeling

Does paired comparisons “likelihood” correspond to a DGP?

  • Plackett-Luce term is at best one term in a DGP
  • Can we derive that P-L objective as an estimator in some stochastic process model?

\[ P(i \rightarrow j | i \rightarrow j \text{ or } j \rightarrow i) \propto \exp(X^j(t)\beta) \]

Todo 3: connection with EPV

Does real estate value capture future possession opportunity?

“Filter EPV”:

  • \( \nu_t = E[\text{points} | D_t] \).
  • \[ \tilde{\nu}_t = \left(\sum_{s_t \in \mathcal{S}} V(s_t)P(s_t|D_t)\right) + \tilde{\nu}_{t + \epsilon}P(\text{ no }s_t \in \mathcal{S} | D_t) \]
  • \( \tilde{\nu}_T = \nu_T = V(s_T) \) when \( T \) is end of possession.
  • \( \mathcal{S} \) are possession-ending actions (baskets, turnovers, fouls, etc.) and \( \tilde{\nu}_t \) gives the residual possession value after accounting for immediate possession endings.
  • \( \tilde{nu}_t \) function of real estate summaries.

Minimal filter EPV example

Made shots and turnovers are only possible terminal outcomes

Time P(made shot) P(TO)
1 0.1 0.5
2 0.8 0.1
3 1 0

Filter EPV calculation: \[ \begin{align} \tilde{\nu}_3 &= 2 \\ \tilde{\nu}_2 &= 0.8 (2) + 0.1 (0) + 0.1 (\tilde{\nu}_3) = 1.8 \\ \tilde{\nu}_1 &= 0.1 (2) + 0.5 (0) + 0.4 (\tilde{\nu}_2) = 0.92 \\ \end{align} \]